Question: Solve for $a$, $ \dfrac{10}{3a} = -\dfrac{2a - 3}{15a} - \dfrac{10}{3a} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3a$ $15a$ and $3a$ The common denominator is $15a$ To get $15a$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{10}{3a} \times \dfrac{5}{5} = \dfrac{50}{15a} $ The denominator of the second term is already $15a$ , so we don't need to change it. To get $15a$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{10}{3a} \times \dfrac{5}{5} = -\dfrac{50}{15a} $ This give us: $ \dfrac{50}{15a} = -\dfrac{2a - 3}{15a} - \dfrac{50}{15a} $ If we multiply both sides of the equation by $15a$ , we get: $ 50 = -2a + 3 - 50$ $ 50 = -2a - 47$ $ 97 = -2a $ $ a = -\dfrac{97}{2}$